Her Royal Highness and her child are both doing well and will remain in hospital overnight, said a spokesman for the palace.
Palace sources said the couple chose to delay the public announcement of the birth to allow them to spend 'quality time' together.
In a statement tonight William said simply: ‘We could not be happier.’
William's father, Charles, the Prince of Wales said this evening: 'Both my wife and I are overjoyed at the arrival of my first grandchild.
'It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy.
'Grandparenthood is a unique moment in anyone’s life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future.'
The tabloids will also be happy for the next seventy or eighty years documenting the ups and downs of royal family. It appears the royal family has once again become popular largely due to the popularity of Wills and Kate.